166 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1919. 
PLATE X. 
(1) Comparison with Oxford plate G,—The differential refrac- 
tion for all the eclipse plates is | 
a= — 46.5, b,d=+82, e=—27.0, 
the differential aberration being zero. 
For the comparison plate G, | 
a= —19.1, 6,d = +0.7, e = — 28.3. 
Hence for X—G, 
a= —2274,b,d= +756 +4 13. 
To these must be added the terms representing change of scale, 
determined from the check plates (Table XIII.), viz. 
a=-+81.2,6, d= — 0.6,e = + 37.3. 
Hence the whole difference X — G, is given by 
a=+38.8, bd=+69, e= +386. 
The first step is to take the measured differences Ax, Ay, and take 
out the parts av + by,dx-+ ey, due to these terms, leaving the cor- 
rected differences A,a, Ayy. 
A,a@ and A,y contain (1) the Einstein displacement, if any and 
(2) the unknown relative orientation of the plates giving rise to 
terms of the form, Av = + 6y, Ay=— Oa. These two parts could 
be separated by a least-squares solution, but in view of the poor 
quality of the material it seems better to adopt a method which 
keeps a better check on possible discordances and shows more clearly 
what is happening. The Einstein displacement in « is small, and 
we might perhaps neglect it altogether in determining @ from the 
g-measures. However, it is clear from preliminary trials that a 
displacement exists—whether the half or the full Einstein dis- 
placement. Hence if we take out three-quarters of the full Einstein 
displacement (2E,) we divide the already slight effect by 4, and at 
the same time deal fairly between the two hypotheses.??. The residuals 
A,a result. 
From the equations A,z=c-+@y we determine by least squares 
the orientation 9, which is found to be +163. Removing the term 
163y we obtain the residuals A,2. . 
Turning to A,y, we correct for the orientation by taking out the 
term —163a, leaving A,y. These values should agree for all the 
stars, except for the displacement and the accidental error. 
ei Ree Liaise I lie SAN aia ili AGE les oe ER I 
“The smaller the displacement provisionally assumed for #, the larger is the displace- 
ment ultimately found from y (see p. 171). 
